Персона:
Леонов, Александр Сергеевич

Организационные подразделения

Организационная единица

Институт общей профессиональной подготовки (ИОПП)

Миссией Института является: фундаментальная базовая подготовка студентов, необходимая для получения качественного образования на уровне требований международных стандартов; удовлетворение потребностей обучающихся в интеллектуальном, культурном, нравственном развитии и приобретении ими профессиональных знаний; формирование у студентов мотивации и умения учиться; профессиональная ориентация школьников и студентов в избранной области знаний, формирование способностей и навыков профессионального самоопределения и профессионального саморазвития. Основными целями и задачами Института являются: обеспечение высококачественной (фундаментальной) базовой подготовки студентов бакалавриата и специалитета; поддержка и развитие у студентов стремления к осознанному продолжению обучения в институтах (САЕ и др.) и на факультетах Университета; обеспечение преемственности образовательных программ общего среднего и высшего образования; обеспечение высокого качества довузовской подготовки учащихся Предуниверситария и школ-партнеров НИЯУ МИФИ за счет интеграции основного и дополнительного образования; учебно-методическое руководство общеобразовательными кафедрами Института, осуществляющими подготовку бакалавров и специалистов по социо-гуманитарным, общепрофессиональным и естественнонаучным дисциплинам, обеспечение единства требований к базовой подготовке студентов в рамках крупных научно-образовательных направлений (областей знаний).

Фамилия

Леонов

Имя

Александр Сергеевич

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Теперь показываю 1 - 10 из 28

Только метаданные
Fast Algorithm for Solving Some Three-Dimensional Inverse Problems of Magnetometry
(2024) Leonov, A. S.; Lukyanenko, D. V.; Yagola, A. G.; Леонов, Александр Сергеевич
Только метаданные
Effective Algorithms for Computing Global and Local Posterior Error Estimates of Solutions to Linear Ill-Posed Problems
(2020) Leonov, A. S.; Леонов, Александр Сергеевич
© 2020, Allerton Press, Inc.We consider extremal problems introduced and investigated earlier by the author for calculating global and local a posteriori error estimates of approximate solutions to ill-posed inverse problems. For linear inverse problems in Hilbert spaces, they consist in maximization of quadratic functionals with two quadratic constraints. The article shows how under certain conditions these problems can be reduced to a problem of maximization of a special (written analytically) differentiable functional with one constraint. New algorithms for calculating global and local a posteriori error estimates based on the solution of these problems are proposed. Their effectiveness is illustrated by numerical experiments on a posteriori error estimation of solutions to the model two-dimensional inverse problem of potential continuation. Experiments show that the proposed algorithms give a posteriori error estimates close to the true error values. Proposed algorithms for global a posteriori error estimation turn out to be more rapid (3 to 5 times) than the previously known algorithms.
Только метаданные
Non-smooth regularization and fast gradient algorithm for micropore structure reconstruction of shale 页岩微米孔隙结构重构的非光滑正则化及快速梯度优化算法
(2020) Wang, Y.; Fan, S.; Lukyanenko, D. V.; Yagola, A. G.; Leonov, A. S.; Леонов, Александр Сергеевич
© 2020, Science Press. All right reserved.The understanding of shale microstructure is the basis of shale gas exploration and development. The traditional detection method is based on the surface damage observation method. In this work, the synchrotron radiation technology of Shanghai Light Source is applied to nondestructive detection of shale structure to obtain projection data, which can avoid X-ray hardening. We use X-ray Computed Tomography (CT) technology to restore images, and propose an L1 norm + TV (total variation) constrained non-smooth regularization method to suppress noise and improve image contrast. Experiments show that this method is effective to reconstruct the microstructure of shale accurately.
Только метаданные
Piecewise uniform regularization for the inverse problem of microtomography with a-posteriori error estimate
(2020) Wang, Y.; Yagola, A. G.; Leonov, A. S.; Леонов, Александр Сергеевич
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. An inverse microtomography problem is under consideration in a class of functions with bounded VH variation. An algorithm for solving this problem is proposed based on Tikhonov's regularization with a special regularizer. The algorithm ensures piecewise uniform convergence of approximate solutions to exact solution of the inverse problem. In addition, the question of a-posteriori error estimate of approximate solutions obtained is considered. A new numerical algorithm for finding this estimate is proposed. Numerical experiments on solving a model inverse problem on the class of functions with bounded VH variation are presented along with the results of a-posteriori error estimate for approximate solutions obtained.
Только метаданные
Numerical Solution of an Inverse Multifrequency Problem in Scalar Acoustics
(2020) Bakushinskii, A. B.; Leonov, A. S.; Леонов, Александр Сергеевич
© 2020, Pleiades Publishing, Ltd.Abstract: A new algorithm is proposed for solving a three-dimensional scalar inverse problem of acoustic sensing in an inhomogeneous medium with given complex wave field amplitudes measured outside the inhomogeneity region. In the case of data measured in a “plane layer,” the inverse problem is reduced via the Fourier transform to a set of one-dimensional Fredholm integral equations of the first kind. Next, the complex amplitude of the wave field is computed in the inhomogeneity region and the desired sonic velocity field is found in this region. When run on a moderate-performance personal computer (without parallelization), the algorithm takes several minutes to solve the inverse problem on rather fine three-dimensional grids. The accuracy of the algorithm is studied numerically as applied to test inverse problems at one and several frequencies simultaneously, and the stability of the algorithm with respect to data perturbations is analyzed.
Только метаданные
Source recovery with a posteriori error estimates in linear partial differential equations
(2020) Leonov, A. S.; Леонов, Александр Сергеевич
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.We consider inverse problems of recovering a source term in initial boundary value problems for linear multidimensional partial differential equations (PDEs) of a general form. A universal stable method suitable for solving such inverse problems is proposed. The method allows one to obtain in the same way approximations to exact sources in different kinds of PDEs using various types of linear supplementary conditions specified with an error. The method is suitable for both spacewise dependent and time-dependent sources. The method consists in preliminary calculation of a special matrix introduced in the article, the matrix of the source inverse problem, and then inverting it using Tikhonov regularization. The matrix can be obtained by solving a number of initial boundary value problems in question with sources in the form of basis functions. Having spent some time for preliminary finding the matrix (for example, by finite element method with a sufficiently detailed grid), we can then use this matrix to quickly solve the inverse problem with various data. The same technique can be applied to solve inverse source problems in linear steady-state PDEs. We also propose an a posteriori error estimation method for the obtained approximate solution and give a numerical algorithm for such estimation. In addition, a relationship is established between the posterior estimate and the lower estimate for the optimal accuracy of solving the inverse problem. The proposed method of solving inverse source problems is illustrated by the numerical solution of model examples for one-dimensional and two-dimensional PDEs of different kinds with a posteriori error estimates.
Только метаданные
Extra-Optimal Methods for Solving Ill-Posed Problems: Survey of Theory and Examples
(2020) Leonov, A. S.; Леонов, Александр Сергеевич
© 2020, Pleiades Publishing, Ltd.Abstract: A new direction in methods for solving ill-posed problems, namely, the theory of regularizing algorithms with approximate solutions of extra-optimal quality is surveyed. A distinctive feature of these methods is that they are optimal not only in the order of accuracy of resulting approximate solutions, but also with respect to a user-specified quality functional. Such functionals can be specified, for example, as an a posteriori estimate of the quality (accuracy) of approximate solutions, a posteriori estimates of various linear functionals of these solutions, and estimates of their mathematical entropy and multidimensional variations of chosen types. The relationship between regularizing algorithms that are extra-optimal and optimal in the order of quality is studied. Issues concerning the practical derivation of a posteriori estimates for the quality of approximate solutions are addressed, and numerical algorithms for finding such estimates are described. The exposition is illustrated by results of numerical experiments.
Только метаданные
Methods for Solving Ill-Posed Extremum Problems with Optimal and Extra-Optimal Properties
(2019) Leonov, A. S.; Леонов, Александр Сергеевич
The notion of the quality of approximate solutions of ill-posed extremum problems is introduced and a posteriori estimates of quality are studied for various solution methods. Several examples of quality functionals which can be used to solve practical extremum problems are given. The new notions of the optimal, optimal-in-order, and extra-optimal qualities of a method for solving extremum problems are defined. A theory of stable methods for solving extremum problems (regularizing algorithms) of optimal-in-order and extra-optimal quality is developed; in particular, this theory studies the consistency property of a quality estimator. Examples of regularizing algorithms of extra-optimal quality for solving extremum problems are given.
Только метаданные
Application of M.Riesz potentials for solving a 3D inverse problem of acoustic sounding
(2019) Leonov, A. S.; Леонов, Александр Сергеевич
© 2019 Published under licence by IOP Publishing Ltd.An inverse coefficient problem for time-dependent 3D wave equation is under consideration. We recover a spatially varying coefficient of this equation knowing special time integrals of the wave eld in an observation domain. The inverse problem has applications to the acoustic sounding, medical imaging, etc. We reduce the inverse problem to a new linear 3D Fredholm integral equation of the first kind in which the integral operator has the form of well-known M.Riesz potentials. The equation has a unique solution for a considered class of coefficients. Assuming a special scheme for recording the data of the inverse problem, we present and substantiate a numerical algorithm of solving this integral equation. The algorithm does not require significant computational resources and a long solution time. It is based on the use of fast Fourier transform. Typical results of solving 3D inverse problem in question on a personal computer for simulated data demonstrate high capabilities of the proposed algorithm.
Только метаданные
A New Algorithm for a Posteriori Error Estimation for Approximate Solutions of Linear Ill-Posed Problems
(2019) Leonov, A. S.; Леонов, Александр Сергеевич
A new algorithm for a posteriori estimation of the error in solutions to linear operator equations of the first kind in a Hilbert space is proposed and justified. The algorithm reduces the variational problem of a posteriori error estimation to two special problems of maximizing smooth functionals under smooth constraints. A finite-dimensional version of the algorithm is considered. The results of a numerical experiment concerning a posteriori error estimation for a typical inverse problem are presented. It is shown experimentally that the computation time required by the algorithm is less, on average, by a factor of 1.4 than in earlier proposed methods.